Data-Driven Model
Take the weather records and forecasts provided for the Data Expo
111 “expo sites” Provided by Data Expo in continential USA
National Weather Service (NWS) forecasts provided
Want to forecast weather from September 1st, 2016 to September 1st, 2017
Need more information in order to create a forecast
Example: Build a one day out forecast for Baltimore, MD
Use the NCDC records as a training set
~30,000 weather stations from the National Climatic Data Center (NCDC)
Use all data before September 1st, 2016 as the training set
New problem: excess of predictors leads to noise and dimensionality issues
Need a method for variable selection
Find the 200 strongest cross-PACF values
Lag the NCDC data by 1 to 4 days (1 day in this example)
Take the 200 stations with the strongest Cross-PACF (lag 1 cross-PACF shown)
Cross-PACF finds the most relevant stations while accounting for smaller lag correlations
Build a density-based hull around the chosen stations
We dont want to take the 200 sites alone, potential noise/variance issues
Two dimensional density hull around the points
This allows us to select only the influential regions of the country
Use all weather stations within the hull to train a model
Use all NCDC stations within the hull as the training set
Build ridge regression model
Were considering LASSO, but we have already performed model selection
Compare Data Driven forecast to NWS forecast, September 2016-2017
Lag 2 Hull Example
Lag 2 Hull Example Selected sites
Use all NCDC stations within the hull as the training set
Build ridge regression model
Maximum Temperature Forecast
Column
Summary of Absolute Forecast Error
| Measure | Avg | Std | Min | Q1 | Med | Q3 | Max |
|---|---|---|---|---|---|---|---|
| NWS Forecast Abs. Error | 3.0658 | 2.6252 | 0.0000 | 1.0000 | 3.0000 | 4.0000 | 17.00 |
| Data Driven Abs. Error | 4.5643 | 3.5070 | 0.0115 | 1.9134 | 4.0288 | 6.2068 | 20.67 |
| Error Difference | 1.4984 | 3.7751 | -12.9181 | -0.5721 | 1.2583 | 3.4627 | 14.67 |
Distribution of Forecast Error
Column
Time Series of Forecast with Observed
Time Series of Forecast comparison
Minimum Temperature Forecast
Column
Summary of Absolute Forecast Error
| Measure | Avg | Std | Min | Q1 | Med | Q3 | Max |
|---|---|---|---|---|---|---|---|
| NWS Forecast Abs. Error | 4.7273 | 3.4719 | 0.0000 | 2.0000 | 4.0000 | 6.5000 | 17.0000 |
| Data Driven Abs. Error | 3.1216 | 2.4693 | 0.0152 | 1.2914 | 2.5373 | 4.3453 | 14.7991 |
| Error Difference | -1.6057 | 3.5674 | -13.7842 | -3.6986 | -1.2547 | 0.6725 | 10.7991 |
Distribution of Forecast Error
Column
Time Series of Forecast with Observed
Time Series of Forecast comparison
Precipitation Forecast
Column
50% Confusion Matrix for Data Driven Forecast
| Weather | Predicted Dry | Predicted Wet |
|---|---|---|
| Dry | 0.649 | 0.069 |
| Wet | 0.160 | 0.122 |
50% Confusion Matrix for NWS Forecast
| Weather | Predicted Dry | Predicted Wet |
|---|---|---|
| Dry | 0.687 | 0.031 |
| Wet | 0.100 | 0.182 |
Column
Comparison of Forecast
NWS Forecast
One Day Out
Two Days Out
Three Days Out
Four Days Out
DD Forecast
One Day Out
Two Days Out
Three Days Out
Four Days Out
Comparison
One Day Out
Two Days Out
Three Days Out
Four Days Out
Minimum Temperature
One Day Out
Two Days Out
Three Days Out
Four Days Out
Precipitation
One Day Out
Two Days Out
Three Days Out
Four Days Out
